Revisiting the constraints on primordial black hole abundance with the isotropic gamma-ray background

We revisit the constraints on primordial black holes (PBHs) in the mass range 10¹³ g - 10¹⁸ g by comparing the 100 keV-5 GeV gamma-ray background with isotropic flux from PBH Hawking radiation (HR). We investigate three effects that may update the constraints on the PBH abundance; (i) reliably calculating the secondary spectra of HR for energy below 5 GeV, (ii) the contributions to the measured isotropic flux from the Galactic PBH HR and that from annihilation radiation due to evaporated positrons, (iii) inclusion of astrophysical background from gamma-ray sources. The conservative constraint is significantly improved by more than an order of magnitude at 2 ×10¹⁶ g ≲M ≲10¹⁷ g over the past relevant work, where the effect (ii) is dominant. After further accounting for the astrophysical background, more than a tenfold improvement extends to a much wider mass range 10¹⁵ g ≲M ≲2 ×10¹⁷ g .